Finite Group Databasebeta

← #29709335

Subgroups — #29709335

Order 15616.

908 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#11758201C211yesmaximal, characteristic, complemented
2#21448541C211yesmaximal, characteristic
3#21448470C211yesmaximal, characteristic, complemented
4#21447303C211yesmaximal, characteristic, complemented
5#21447240C211yesmaximal, characteristic, complemented
6#21447202C211yesmaximal, characteristic, complemented
7#21447189C211yesmaximal, characteristic, complemented
8#21447133C211yesmaximal, characteristic, complemented
9#21447132C211yesmaximal, characteristic, complemented
10#21447052C211yesmaximal, characteristic
11#21446905C211yesmaximal, characteristic
12#21445679C211yesmaximal, characteristic, complemented
13#21445645C211yesmaximal, characteristic, complemented
14C4×#14519698C211yesmaximal, characteristic, complemented
15C2×C61×#440C211yesmaximal, characteristic, complemented
16C22×#11758201C2211yescharacteristic
17C2×#14519773C2211yescharacteristic
18C2×C4×D244C2211yescharacteristic
19C4×#11758201—24no—
20C2×#14519708C2211yescharacteristic
21C2×#14519706C2211yescharacteristic
22C2×#14519706C2211yescharacteristic
23C2×#14519701C2211yescharacteristic
24C2×#14519699C2211yescharacteristic
25C2×#14519699C2211yescharacteristic
26C2×#14519698C2211yescharacteristic
27C2×#14519698C2211yescharacteristic
28C2×#14519697C2211yescharacteristic
29C2×C4×#92418C2211yescharacteristic
30#16839669C2211yescharacteristic
31#16839669C2211yescharacteristic
32#16839665C2211yescharacteristic
33#16839663C2211yescharacteristic
34#16839661C2211yescharacteristic
35#16839661C2211yescharacteristic
36#16839648—21no—
37#16839648—21no—
38#16839641—21no—
39#16839641—21no—
40#16839638—21no—
41#16839638—21no—
42#16839630—21no—
43#16839628—21no—
44#16839627C2211yescharacteristic
45C4×C4⋊Dic61C2211yescharacteristic
46#16839608C2211yescharacteristic
47#16839525C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839516C2211yescharacteristic
52#16839516C2211yescharacteristic
53C22×SD16×C61C2211yescharacteristic
54C2×C4×Q8×C61C2211yescharacteristic
55C2×C4×D4×C61C2211yescharacteristic
56C61×#440—24no—
57C2×#107×C61C2211yescharacteristic
58C2×#103×C61C2211yescharacteristic
59C2×#102×C61C2211yescharacteristic
60C2×#97×C61C2211yescharacteristic
61C22×D244C2311yescharacteristic
62C22×C22⋊D61—21no—
63C22×C22⋊D61—21no—
64C22×C4×D61—21no—
65C2×#11758201—22no—
66C2×#11758201—22no—
67C2×#11758201—22no—
68C22×#92418C2311yescharacteristic
69C22×#92418C2311yescharacteristic
70#14519773—22no—
71#14519773—22no—
72C4×D244—22no—
73C4×D244—22no—
74C2×C4⋊Dic61—21no—
75C2×C4⋊Dic61—21no—
76C2×C4⋊Dic61C2311yescharacteristic
77C2×C4⋊Dic61C2311yescharacteristic
78C2×C4⋊Dic61C2311yescharacteristic
79C2×C22⋊Dic61—21no—
80C2×C22⋊Dic61—21no—
81C2×#11758198—21no—
82C2×#11758198—21no—
83C2×#11758198—21no—
84C2×C4×Dic61—21no—
85C2×C4×Dic61C2311yescharacteristic
86C2×C4×Dic61C2311yescharacteristic
87#14519708—22no—
88#14519706—22no—
89#14519706—22no—
90#14519701—22no—
91#14519699—22no—
92#14519699—22no—
93#14519698—22no—
94#14519698—22no—
95#14519697—22no—
96C4×#92418—22no—
97#14519684—21no—
98#14519684—21no—
99#14519684—21no—
100#14519684—21no—
101#14519684—21no—
102#14519684—21no—
103#14519684—21no—
104#14519684—21no—
105#14519684—21no—
106#14519684D411yescharacteristic
107#14519684D411yescharacteristic
108#14519684D411yescharacteristic
109#14519684D411yescharacteristic
110C22×Q8×C61C2311yescharacteristic
111C22×D4×C61C2311yescharacteristic
112C23×C4×C61—21no—
113C2×SD16×C61—22no—
114C2×SD16×C61—22no—
115C2×SD16×C61—22no—
116C22×C8×C61C2311yescharacteristic
117C22×C8×C61C2311yescharacteristic
118C4×Q8×C61—22no—
119C4×Q8×C61D414yescomplemented
120C4×D4×C61—22no—
121C4×D4×C61—22no—
122C2×C4⋊C4×C61—21no—
123C2×C4⋊C4×C61C2311yescharacteristic
124C2×C4⋊C4×C61C2311yescharacteristic
125C2×C22⋊C4×C61—21no—
126C2×C42×C61—21no—
127C2×C42×C61C2311yescharacteristic
128#107×C61—22no—
129#103×C61—22no—
130#102×C61—22no—
131#97×C61—22no—
132C24×C61—21no—
133C23×D61—21no—
134C2×Q8×C61—21no—
135C2×Q8×C61—21no—
136C2×Q8×C61—21no—
137C2×Q8×C61—21no—
138C2×Q8×C61—21no—
139C2×Q8×C61C2×D412yes—
140C2×D4×C61—21no—
141C2×D4×C61—21no—
142C2×D4×C61—21no—
143C2×D4×C61—21no—
144C2×D4×C61—21no—
145C2×D4×C61#4112yes—
146C22×C4×C61—21no—
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61—42no—
150C22×C4×C61—81no—
151C22×C4×C61—81no—
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61C2411yescharacteristic
155C2×C22⋊D61—24no—
156C2×C22⋊D61—24no—
157C2×C22⋊D61—81no—
158C2×C22⋊D61—81no—
159C2×C22⋊D61—81no—
160C2×C22⋊D61—81no—
161C22×Dic61—21no—
162C22×Dic61—21no—
163C22×Dic61—21no—
164C22×Dic61C2×D411yescharacteristic
165C22×Dic61C2×D411yescharacteristic
166C22×Dic61C2×D411yescharacteristic
167C22×Dic61C2×D411yescharacteristic
168C2×D244—21no—
169C2×D244—21no—
170C2×D244—21no—
171C2×D244—21no—
172C2×D244—21no—
173C2×D244#4112yes—
174C2×C4×D61—42no—
175C2×C4×D61—81no—
176C2×C4×D61—81no—
177SD16×C61—28no—
178C2×C8×C61—21no—
179C2×C8×C61—21no—
180C2×C8×C61—21no—
181C2×C8×C61—21no—
182C2×C8×C61—21no—
183C2×C8×C61#4112yes—
184C4⋊C4×C61—24no—
185C4⋊C4×C61—21no—
186C4⋊C4×C61—21no—
187C4⋊C4×C61—21no—
188C4⋊C4×C61C2×D412yes—
189C22⋊C4×C61—42no—
190C42×C61—24no—
191C42×C61C2×D412yes—
192C42×C61#4112yes—
193C22⋊Dic61—81no—
194C22⋊Dic61—81no—
195#11758201—28no—
196#11758198—42no—
197#11758198—81no—
198#11758198—81no—
199C4⋊Dic61—21no—
200C4⋊Dic61—21no—
201C4⋊Dic61—21no—
202C4⋊Dic61—21no—
203C4⋊Dic61—21no—
204C4⋊Dic61—21no—
205C4⋊Dic61—81no—
206C4⋊Dic61—81no—
207C4×Dic61—21no—
208C4×Dic61—21no—
209C4×Dic61—21no—
210C4×Dic61—21no—
211C4×Dic61—81no—
212C2×#92418—21no—
213C2×#92418—21no—
214C2×#92418—21no—
215C2×#92418—21no—
216C2×#92418—21no—
217C2×#92418#4112yes—
218C23×C61—22no—
219C23×C61—41no—
220C23×C61—41no—
221C23×C61—41no—
222C23×C61—41no—
223C23×C61—41no—
224C23×C61—41no—
225C23×C61C22×D411yescharacteristic
226C22×D61—22no—
227C22×D61—41no—
228C22×D61—41no—
229C22×D61—41no—
230C22×D61—41no—
231C22×D61—41no—
232C22×D61—41no—
233Q8×C61—22no—
234Q8×C61—22no—
235Q8×C61—41no—
236Q8×C61—41no—
237D4×C61—22no—
238D4×C61—22no—
239D4×C61—41no—
240D4×C61—41no—
241C2×C4×C61—21no—
242C2×C4×C61—21no—
243C2×C4×C61—21no—
244C2×C4×C61—21no—
245C2×C4×C61—22no—
246C2×C4×C61—22no—
247C2×C4×C61—41no—
248C2×C4×C61—41no—
249C2×C4×C61—41no—
250C2×C4×C61—41no—
251C2×C4×C61—41no—
252C2×C4×C61—41no—
253C2×C4×C61—41no—
254C2×C4×C61—84no—
255C2×C4×C61#12112yes—
256C2×C4×C61#12112yes—
257C2×C4×C61C22×D411yescharacteristic
258C2×C4×C61C2×#4111yescharacteristic
259C2×C4×C61C2×#4111yescharacteristic
260C2×C4×C61C2×#4111yescharacteristic
261C2×C4×C61C2×#4111yescharacteristic
262C2×C4×C61C2×#4111yescharacteristic
263C22⋊D61—84no—
264C22⋊D61—84no—
265C2×Dic61—21no—
266C2×Dic61—21no—
267C2×Dic61—21no—
268C2×Dic61—21no—
269C2×Dic61—21no—
270C2×Dic61—21no—
271C2×Dic61—21no—
272C2×Dic61—21no—
273C2×Dic61—21no—
274C2×Dic61—21no—
275C2×Dic61—21no—
276C2×Dic61—21no—
277C2×Dic61—41no—
278C2×Dic61—41no—
279C2×Dic61—41no—
280C2×Dic61—41no—
281C2×Dic61—41no—
282C2×Dic61—41no—
283C2×Dic61—41no—
284C2×Dic61—41no—
285C2×Dic61—41no—
286D244—22no—
287D244—22no—
288D244—41no—
289D244—41no—
290C4×D61—84no—
291C8×C61—22no—
292C8×C61—41no—
293#92418—22no—
294#92418—41no—
295#23690—611nomaximal, Sylow
296C22×C61—42no—
297C22×C61—42no—
298C22×C61—42no—
299C22×C61—81no—
300C22×C61—81no—
301C22×C61—81no—
302C22×C61—81no—
303C22×C61C2×#12111yescharacteristic
304C22×C61#52511yescharacteristic
305C22×C61#53211yescharacteristic
306C22×C61#57611yescharacteristic
307C22×C61#57711yescharacteristic
308C22×C61#57711yescharacteristic
309C22×C61#57711yescharacteristic
310C2×D61—42no—
311C2×D61—42no—
312C2×D61—42no—
313C2×D61—81no—
314C2×D61—81no—
315C2×D61—81no—
316C2×D61—81no—
317C4×C61—22no—
318C4×C61—22no—
319C4×C61—42no—
320C4×C61—42no—
321C4×C61—81no—
322C4×C61#52511yescharacteristic
323C4×C61#52511yescharacteristic
324C4×C61#52911yescharacteristic
325C4×C61#52911yescharacteristic
326Dic61—41no—
327Dic61—41no—
328Dic61—41no—
329Dic61—41no—
330Dic61—81no—
331Dic61—81no—
332Dic61—81no—
333C2×#440D6111yescharacteristic, complemented
334C2×C4×SD16—611no—
335#2328—611no—
336#2320—611no—
337#2085—611no—
338#2074—611no—
339#2067—611no—
340#2065—611no—
341#2055—611no—
342#2055—611no—
343#2041—611no—
344#2014—611no—
345#1768—611no—
346#1762—611no—
347C4×#102—611no—
348C2×C61—82no—
349C2×C61#239211yescharacteristic
350C2×C61#304311yescharacteristic
351C2×C61#304511yescharacteristic
352C2×C61#311811yescharacteristic
353C2×C61#312311yescharacteristic
354C2×C61#317411yescharacteristic
355C2×C61#317911yescharacteristic
356D61—82no—
357C22×SD16—611no—
358C22×SD16C2×D6111yescharacteristic
359C2×#127—611no—
360C2×C4×Q8C2×D6111yescharacteristic
361C2×C4×D4—611no—
362C2×C4×D4C2×D6111yescharacteristic
363#440—24no—
364C4×SD16—1224no—
365C2×#107C2×D6111yescharacteristic
366C2×#106—611no—
367C2×C4⋊C8—611no—
368C2×C4⋊C8—611no—
369C2×#103—611no—
370C2×#103C2×D6111yescharacteristic
371C2×#102—611no—
372C2×#102—611no—
373C2×#102—611no—
374C2×#102—611no—
375C2×#102—611no—
376C2×#102C2×D6111yescharacteristic
377C2×#97C2×D6111yescharacteristic
378C2×C4×C8—611no—
379#391—611no—
380#391—611no—
381#390—611no—
382#390—611no—
383#389—611no—
384#389—611no—
385#387—1221no—
386#387—1221no—
387#386—1221no—
388#386—1221no—
389#386—1221no—
390#386—1221no—
391#383—1221no—
392#382—611no—
393#382—1221no—
394C4×C4⋊C4—611no—
395#376—611no—
396#340—611no—
397#340—611no—
398#340—611no—
399#340—611no—
400#336—611no—
401#336—611no—
402C61#2369011yescharacteristic, complemented, Sylow
403C22×Q8C22×D6111yescharacteristic
404C22×D4—611no—
405C22×D4—1221no—
406C22×D4—1221no—
407C22×D4C22×D6111yescharacteristic
408C23×C4—21no—
409C23×C4—1221no—
410C2×SD16—22no—
411C2×SD16—22no—
412C2×SD16—22no—
413C2×SD16—1222no—
414C2×SD16—1222no—
415C2×SD16—1222no—
416C22×C8—611no—
417C22×C8—611no—
418C22×C8C22×D6111yescharacteristic
419C22×C8C22×D6111yescharacteristic
420#127—1222no—
421#127—1222no—
422C4×Q8—22no—
423C4×Q8C22⋊D6114yescomplemented
424C4×D4—22no—
425C4×D4—22no—
426C4×D4—1222no—
427C4×D4—1222no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—611no—
430C2×C4⋊C4—611no—
431C2×C4⋊C4—611no—
432C2×C4⋊C4—1221no—
433C2×C4⋊C4—1221no—
434C2×C4⋊C4C22×D6111yescharacteristic
435C2×C4⋊C4C22×D6111yescharacteristic
436C2×C22⋊C4—21no—
437C2×C22⋊C4—1221no—
438C2×C22⋊C4—1221no—
439C2×C22⋊C4—1221no—
440C2×C22⋊C4—1221no—
441C2×C22⋊C4—1221no—
442C2×C42—21no—
443C2×C42—611no—
444C2×C42—611no—
445C2×C42—1221no—
446C2×C42C22×D6111yescharacteristic
447#107—22no—
448#106—1222no—
449C4⋊C8—1222no—
450C4⋊C8—1222no—
451#103—22no—
452#103—1222no—
453#102—22no—
454#102—1222no—
455#102—1222no—
456#102—1222no—
457#102—1222no—
458#102—1222no—
459#97—22no—
460C4×C8—1222no—
461#95—611no—
462#95—611no—
463#95—611no—
464#95—611no—
465#95—1221no—
466#95—1221no—
467#95—1221no—
468#95—1221no—
469#95—1221no—
470#95—1221no—
471#95—1221no—
472#95—1221no—
473#95—1221no—
474C24—21no—
475C24—1221no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8C2×C22⋊D6112yes—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—612no—
488C2×D4—1224no—
489C2×D4—1224no—
490C2×D4—1221no—
491C2×D4—1221no—
492C2×D4—1221no—
493C2×D4—1221no—
494C2×D4—1221no—
495C2×D4—4881no—
496C2×D4—4881no—
497C2×D4—4881no—
498C2×D4—4881no—
499C2×D4#1175822212yes—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—42no—
504C22×C4—81no—
505C22×C4—81no—
506C22×C4—611no—
507C22×C4—611no—
508C22×C4—611no—
509C22×C4—611no—
510C22×C4—1221no—
511C22×C4—1221no—
512C22×C4—1221no—
513C22×C4—4881no—
514C22×C4—4881no—
515C22×C4—2442no—
516C22×C4D4×D6111yescharacteristic
517C22×C4D4×D6111yescharacteristic
518C22×C4C23×D6111yescharacteristic
519SD16—28no—
520SD16—1228no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—612no—
527C2×C8—1221no—
528C2×C8—1221no—
529C2×C8—1221no—
530C2×C8—1221no—
531C2×C8—1221no—
532C2×C8#1175822212yes—
533C4⋊C4—21no—
534C4⋊C4—24no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—1221no—
538C4⋊C4—1221no—
539C4⋊C4—1221no—
540C4⋊C4—1221no—
541C4⋊C4—1221no—
542C4⋊C4—1221no—
543C4⋊C4—4881no—
544C4⋊C4—4881no—
545C4⋊C4C2×C22⋊D6112yes—
546C22⋊C4—42no—
547C22⋊C4—4881no—
548C22⋊C4—4881no—
549C22⋊C4—4881no—
550C22⋊C4—4881no—
551C22⋊C4—2442no—
552C42—24no—
553C42—1221no—
554C42—1221no—
555C42—1221no—
556C42—1221no—
557C42—4881no—
558C42#1175822412yes—
559C42C2×C22⋊D6112yes—
560C23—22no—
561C23—41no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23—41no—
566C23—41no—
567C23—1222no—
568C23—2441no—
569C23—2441no—
570C23—2441no—
571C23—2441no—
572C23—2441no—
573C23—2441no—
574C23C2×D4×D6111yescharacteristic
575Q8—22no—
576Q8—22no—
577Q8—41no—
578Q8—41no—
579D4—22no—
580D4—22no—
581D4—41no—
582D4—41no—
583D4—1222no—
584D4—1222no—
585D4—4884no—
586D4—4884no—
587D4—2441no—
588D4—2441no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—84no—
603C2×C4—1221no—
604C2×C4—1221no—
605C2×C4—1221no—
606C2×C4—1221no—
607C2×C4—1221no—
608C2×C4—1221no—
609C2×C4—1221no—
610C2×C4—1221no—
611C2×C4—1221no—
612C2×C4—1221no—
613C2×C4—1221no—
614C2×C4—1221no—
615C2×C4—4884no—
616C2×C4—2441no—
617C2×C4—2441no—
618C2×C4—2441no—
619C2×C4—2441no—
620C2×C4—2441no—
621C2×C4—2441no—
622C2×C4—2441no—
623C2×C4—2441no—
624C2×C4—2441no—
625C2×C4#1451974912yes—
626C2×C4#1451974912yes—
627C2×C4C22×C22⋊D6111yescharacteristic
628C2×C4#41×D6111yescharacteristic
629C2×C4#41×D6111yescharacteristic
630C2×C4C2×#1175822411yescharacteristic
631C2×C4C2×#1175822211yescharacteristic
632C2×C4C2×#1175822211yescharacteristic
633C8—22no—
634C8—41no—
635C8—1222no—
636C8—2441no—
637C22—42no—
638C22—42no—
639C22—42no—
640C22—81no—
641C22—81no—
642C22—81no—
643C22—81no—
644C22—4881no—
645C22—4881no—
646C22—4881no—
647C22—4881no—
648C22—2442no—
649C22—2442no—
650C22—2442no—
651C22C2×#1451974911yescharacteristic
652C22#1684027111yescharacteristic
653C22#1684030911yescharacteristic
654C22#1684056611yescharacteristic
655C22#1684057111yescharacteristic
656C22#1684057111yescharacteristic
657C22#1684057211yescharacteristic
658C4—22no—
659C4—22no—
660C4—42no—
661C4—42no—
662C4—81no—
663C4—4881no—
664C4—4881no—
665C4—4881no—
666C4—2441no—
667C4—2441no—
668C4—2441no—
669C4—2441no—
670C4#1684026911yescharacteristic
671C4#1684027311yescharacteristic
672C4#1684029211yescharacteristic
673C4#1684029411yescharacteristic
674C2—82no—
675C2—4882no—
676C2#2144906111yescharacteristic
677C2#2145534211yescharacteristic
678C2#2145536211yescharacteristic
679C2#2145600711yescharacteristic
680C2#2145607011yescharacteristic
681C2#2145644511yescharacteristic
682C2#2145650011yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#440C2
socleC23×C61C22×D4
prime radicalC2×#14519773C22
hypercenterC2×#440D61
hypocenterC61#23690
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C4×#11758201C2semidirect
3. #21448470C2semidirect
4. #21447303C2semidirect
5. #21447240C2semidirect
6. #21447202C2semidirect
7. #21447189C2semidirect
8. #21447133C2semidirect
9. #21447132C2semidirect
12. #21445679C2semidirect
13. #21445645C2semidirect
14. C4×#14519698C2semidirect
15. C2×C61×#440C2semidirect
119. C4×Q8×C61D4semidirect
333. C2×#440D61semidirect
402. C61#23690semidirect
423. C4×Q8C22⋊D61semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C4×#117582012
#214485412
#214484702
#214473032
#214472402
#214472022
#214471892
#214471332
#214471322
#214470522
#214469052
#214456792
#214456452
C4×#145196982
C2×C61×#4402
#2369061